Improved unbiased estimators in adaptive cluster sampling

Summary.  The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics—not necessarily minimal—are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.     

Defining equations for two-level factorial designs

Defining equations are introduced in the context of two-level factorial designs and they are shown to provide a concise specification of both regular and nonregular designs. The equations are used to find orthogonal arrays of high strength and some optimal designs. The latter optimal designs are formed in a new way by augmenting notional orthogonal arrays which are allowed to have some runs with a negative number of replicates before augmentation. Defining equations are also shown to be useful when the factorial design is blocked.     

Design-based analysis of embedded experiments with applications in the Dutch Labour Force Survey

Summary.  Previous research has proposed a design-based analysis procedure for experiments that are embedded in complex sampling designs in which the ultimate sampling units of an on-going sample survey are randomized over different treatments according to completely randomized designs or randomized block designs. Design-based Wald and t -statistics are applied to test whether sample means that are observed under various survey implementations are significantly different. This approach is generalized to experimental designs in which clusters of sampling units are randomized over the different treatments. Furthermore, test statistics are derived to test differences between ratios of two sample estimates that are observed under alternative survey implementations. The methods are illustrated with a simulation study and real life applications of experiments that are embedded in the Dutch Labour Force Survey. The functionality of a software package that was developed to conduct these analyses is described.     

Testing order restricted hypotheses with proportional hazards

Inferences for survival curves based on right censored continuous or grouped data are studied. Testing homogeneity with an ordered restricted alternative and testing the order restriction as the null hypothesis are considered. Under a proportional hazards model, the ordering on the survival curves corresponds to an ordering on the regression coefficients. Approximate likelihood methods are obtained by applying order restricted procedures to the estimates of the regression coefficients. Ordered analogues to the log rank test which are based on the score statistics are considered also. Chi-bar-squared distributions, which have been studied extensively, are shown to provide reasonable approximations to the null distributions of these tests statistics. Using Monte Carlo techniques, the powers of these two types of tests are compared with those that are available in the literature.     

Estimation of Covariate Distribution with Capture–Recapture Data

The main purpose of this article is to estimate the underlying covariate distribution with a biased capture–recapture sample. Two procedures are proposed, and the derived estimates are found to be consistent and asymptotically normal. The proposed methods are compared and are shown to perform well in most circumstances via simulation study, and are applied to a real example.     

Estimation of the Parameters of the Birnbaum–Saunders Distribution

Some alternative estimators to the maximum likelihood estimators of the two parameters of the Birnbaum–Saunders distribution are proposed. Most have high efficiencies as measured by root mean square error and are robust to departure from the model as well as to outliers. In addition, the proposed estimators are easy to compute. Both complete and right-censored data are discussed. Simulation studies are provided to compare the performance of the estimators.     

SELECTION OF WEIGHTS FOR WEIGHTED MODEL AVERAGING

We address the task of choosing prior weights for models that are to be used for weighted model averaging. Models that are very similar should usually be given smaller weights than models that are quite distinct. Otherwise, the importance of a model in the weighted average could be increased by augmenting the set of models with duplicates of the model or virtual duplicates of it. Similarly, the importance of a particular model feature (a certain covariate, say) could be exaggerated by including many models with that feature. Ways of forming a correlation matrix that reflects the similarity between models are suggested. Then, weighting schemes are proposed that assign prior weights to models on the basis of this matrix. The weighting schemes give smaller weights to models that are more highly correlated. Other desirable properties of a weighting scheme are identified, and we examine the extent to which these properties are held by the proposed methods. The weighting schemes are applied to real data, and prior weights, posterior weights and Bayesian model averages are determined. For these data, empirical Bayes methods were used to form the correlation matrices that yield the prior weights. Predictive variances are examined, as empirical Bayes methods can result in unrealistically small variances.     

An evaluation of methods for testing hypotheses relating to two endpoints in a single clinical trial

The issues and dangers involved in testing multiple hypotheses are well recognised within the pharmaceutical industry. In reporting clinical trials, strenuous efforts are taken to avoid the inflation of type I error, with procedures such as the Bonferroni adjustment and its many elaborations and refinements being widely employed. Typically, such methods are conservative. They tend to be accurate if the multiple test statistics involved are mutually independent and achieve less than the type I error rate specified if these statistics are positively correlated. An alternative approach is to estimate the correlations between the test statistics and to perform a test that is conditional on those estimates being the true correlations. In this paper, we begin by assuming that test statistics are normally distributed and that their correlations are known. Under these circumstances, we explore several approaches to multiple testing, adapt them so that type I error is preserved exactly and then compare their powers over a range of true parameter values. For simplicity, the explorations are confined to the bivariate case. Having described the relative strengths and weaknesses of the approaches under study, we use simulation to assess the accuracy of the approximate theory developed when the correlations are estimated from the study data rather than being known in advance and when data are binary so that test statistics are only approximately normally distributed.     

On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

Two types of shifted geometric integer valued autoregressive models of order one (SGINAR(1)) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR(1) models.     

Some New Bounds on the Probability of Extinction of a Galton–Watson Process with Numerical Comparisons

Some new upper and lower bounds for the extinction probability of a Galton–Watson process are presented. They are very easy to compute and can be used even if the offspring distribution has infinite variance. These new bounds are numerically compared to previously discussed bounds. Some definite guidelines are given concerning when these new bounds are preferable. Some open problems are also discussed.     

Low-order spatially-distinct latin squares

The order three to five spatially-distinct Latin squares, and the order three to six spatially-distinct Latin square treatment designs are listed. Some statistical results are given. Designs for 4, 5 and 6 treatments that were found previously to be robust to a linear by linear interacrion are shown to be optimal. Designs with good neighbour balanced are also considered.     

Some Results on Modeling Biological Sequences and Web Navigation with a Semi Markov Chain

In the article, the entrance probabilities and the probability distribution of the number of transitions to a state are studied to provide some answers to questions related to state occupancies for the semi Markov model. Biological sequences and Web navigation are two cases that initially seem to be different but to a certain extent they do have similarities. Two main aspects of word occurrences in biological sequences are: (a) where do they occur and (b) how many times do they occur. In Web navigation the similar questions are (a) when a node is visited and (b) how many times a node is visited. So, the theoretical results of this study are applied to model these two cases and derive distributions of word location or node occurrence and frequency of occurrences. Rewards/costs are included in the Web navigation model and analytic forms for the means, variances, and moments of total interval rewards/costs are provided.     

Tracing studies and analysis of the effect of loss to follow-up on mortality estimation from patient registry data

Summary. Before patient registries are used for studies of the long-term mortality that is associated with chronic medical conditions, the potential bias resulting from patients who become lost to follow-up must be investigated. A study design, used for a systemic lupus erythematosus patient registry, is described. The design involves tracing patients who are defined as 'lost to follow-up' according to specific criteria. This provides supplementary information on the mortality experience of patients who are lost to (regular) follow-up. Some methods of analysis are described, based on comparing the mortality experience of patients when under regular follow-up with the experience of patients after they are deemed to be lost to follow-up. The effect of loss to follow-up, death reporting and visits to the clinic on estimation procedures is illustrated and recommendations are made for patient registries which are to be used in mortality studies.     

When there are outliers in the carriers:the univariate case

Robust regression estimators studied to date are robust against non-normal distributions of the errors only If the carriers ‘Independent variables’ do not also contain outliers. Several alternative estimators that are robust even 1f there are outliers in the carriers are studied. Two estimators seem to be preferable, but even these can be very Inefficient ‘relative to least squares’ If the errors are normally distributed.     

Simple random sample equivalent survey designs reducing undesirable units from a finite population

In this paper, we consider fixed size sampling plans for which the first order inclusion probabilities are identical for all units and the second order inclusion probabilities are constant for every pair-wise unit. The statistical conditions are identified under which these plans are equivalent to the usual simple random sampling plan. These sampling plans are constructed to reduce undesirable units.     

A Semiparametric Bayesian Model for Circular-Linear Regression

Circular data are observations that are represented as points on a unit circle. Times of day and directions of wind are two such examples. In this work, we present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is useful especially when the likelihood surface is ill behaved. Markov chain Monte Carlo techniques are used to fit the proposed model and to generate predictions. The method is illustrated using an environmental data set.     

Homogeneity of Two Straight Lines: Equivalence Approach Using Fitted Regressions

The paper examines the homogeneity of a pair of straight lines, regarded as the expected values of two different linear regressions, from an equivalence point of view. This seems more appropriate than the usual testing of the null hypothesis of homogeneity when the aim is to establish that the lines are close to homogeneous. Upper confidence bounds on the maximum difference between the lines are based on the usual least squares regression estimators, assuming normal distributions. These bounds are constructed for fixed points, or over a fixed interval, and it is concluded that the lines are 1-homogeneous if the bounds are not greater than 1: Also, intervals are constructed over which the lines are concluded to be 1-homogeneous.     

Temporal pattern in number of staff on sick leave: the effect of downsizing

Summary.  The pattern of absenteeism in the downsizing process of companies is a topic in focus in economics and social science. A general question is whether employees who are frequently absent are more likely to be selected to be laid off or in contrast whether employees to be dismissed are more likely to be absent for the remaining time of their working contract. We pursue an empirical and microeconomic investigation of these theses. We analyse longitudinal data that were collected in a German company over several years. We fit a semiparametric transition model based on a mixture Poisson distribution for the days of absenteeism per month. Prediction intervals are considered and the primary focus is on the period of downsizing. The data reveal clear evidence for the hypothesis that employees who are to be laid off are more frequently absent before leaving the company. Interestingly, though, no clear evidence is seen that employees being selected to leave the company are those with a bad absenteeism profile.     

Unit root tests and dramatic shifts with infinite variance processes

A model which explains data that is subject to sudden structural changes of unspecified nature is presented. The structural shifts are generated by a random walk component whose innovations belong to the normal domain of attraction of a symmetric stable law. To test the model against the stationarity case, several non-parametric, and regression-based statistics are studied. The non-parametric tests are a generalization of the variance ratio test to innovations with heavy-tailed distributions. The tests are consistent and shown to have good finite sample size and power properties and are applied to a set of economic variables.     

Closed-form approximate tolerance intervals for some general linear models and comparison studies

The problems of constructing tolerance intervals (TIs) in random effects model and in a mixed linear model are considered. The methods based on the generalized variable (GV) approach and the one based on the modified large sample (MLS) procedure are evaluated with respect to coverage probabilities and expected width in various setups using Monte Carlo simulation. Our comparison studies indicate that the TIs based on the MLS procedure are comparable to or better than those based on the GV approach. As the MLS TIs are in closed-form, they are easier to compute than those based on the GV approach. TIs for a two-way nested model are also derived using the MLS method, and their merits are evaluated using simulation. The procedures are illustrated using a practical example.